$\"\"$

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Let the length of a high school soccer field is $\"\"$ .

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The width of a high school soccer field is 45 yards shorter than its length, so the width is $\"\"$ .

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The area of the rectangle is $\"\"$ .

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The value of $\"\"$ are substitute in the equation, $\"\"$ .

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$\"\"$

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Apply distributive property: $\"\"$ .

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$\"\"$

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The expression for area of the high school soccer field is $\"\"$ . $\"\"$

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The area of the high school soccer field is $\"\"$ .

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The value of $\"\"$ are substitute in the equation, $\"\"$ .

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$\"\"$

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Subtract 9000 from each side.

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$

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$\"\"$ $\"\"$

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Apply zero product property: $\"\"$ .

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$\"\"$

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Solve the first equation, $\"\"$ .

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Solve the second equation, $\"\"$ .

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The dimensions are never express in negative sign.So the value of $\"\"$ is taken only.

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The length of the rectangle is 120 yards its width is $\"\"$ . $\"\"$

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(a) The expression for area of the high school soccer field is $\"\"$ .

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(b) The length of the rectangle is 120 yards its width is $\"\"$ .